Classification of no-signaling correlation and the "guess your neighbor's input" game

We formulate a series of nontrivial equalities which are satisfied by all no-signaling correlations, meaning that no faster-than-light communication is allowed with the resource of these correlations. All quantum and classical correlations satisfy these equalities since they are no-signaling. By applying these equalities, we provide a general framework for solving the multipartite "guess your neighbor's input" (GYNI) game, which is naturally no-signaling but shows conversely that general no-signaling correlations are actually more nonlocal than those allowed by quantum mechanics. We confirm the validity of our method for the number of players from 3 up to 19, thus providing convincing evidence that it works for the general case. In addition, we solve analytically the tripartite GYNI and obtain a computable measure of supraquantum correlations. This result simplifies the defined optimization procedure to an analytic formula, thus characterizing explicitly the boundary between quantum and supraquantum correlations. In addition, we show that the gap between quantum and no-signaling boundaries containing supraquantum correlations can be closed by local orthogonality conditions in the tripartite case. Our results provide a computable classification of no-signaling correlations.